The Green function variational approximation: Significance of physical constraints

TL;DR

This paper introduces a variational approximation method for calculating spectral properties of doped charge in CuF3, emphasizing the importance of physical constraints like exclusion of crossing diagrams and double occupation.

Contribution

The paper develops a dependable, flexible variational approximation method that systematically includes physical constraints, improving upon the Self-Consistent Born Approximation for polaron spectral analysis.

Findings

Physical constraints significantly affect spectral functions.

The variational approximation provides deep physical insights.

Excluding crossing diagrams improves spectral accuracy.

Abstract

We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent Dyson expansions and solving the resulting set of equations. This method, dubbed the variational approximation, is both very dependable and flexible, since it is a systematic expansion with precise control over elementary physical processes. It allows for deep insight into the underlying physics of polaron formation as well as for inclusion of many physical constraints, such as excluding crossing diagrams and double occupation constraint, which are not included in the Self-Consistent Born Approximation. Here we examine the role and importance of such constraints by analyzing various spectral functions obtained in second order VA.